It has been known that single particles “co-produced” from independent sources may show interference. This phenomenon, namely, “Pfleegor-Mandel interference”, was demonstrated with photons [1], and the interference takes place because in certain circumstances we do not know from which source the detected particle originated. Here I point out that this phenomenon generates a serious paradox when it is applied to a charged particle interacting with a localized magnetic flux. I discuss the origin of this paradox, and attempt to resolve it. A realistic experimental setup with superconducting Y-junction is proposed, which can settle the issue of dynamic quantum nonlocality in the electromagnetic interaction manifested in the Aharonov-Bohm effect [2].